Let R Be the Region in the First Quadrant Bounded $\int _ { R } \sqrt { x + 2 y } d A$

question 20

Essay

Let R be the region in the first quadrant bounded by the x- and y-axes and the line x + y = 7.Evaluate $\int _ { R } \sqrt { x + 2 y } d A$ exactly and then give an answer rounded to 4 decimal places.

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Definitions:

Internal Improvements

Internal improvements refer to public works and infrastructure projects, such as roads, canals, and railroads, financed and constructed by the government to facilitate commerce and communication within a country.

American System

An economic plan advocated by Henry Clay in the early 19th century, emphasizing support for a national bank, high tariffs, and internal improvements to foster national economic growth.

Panic of 1819

The first major financial crisis in the United States, which occurred due to a sudden collapse of the economy, leading to bank failures and unemployment.

European Market

The combined economies of European countries, often referring to the single market in the context of the European Union.